A method and system for hierarchical thermal control of an X-ray telescope support truss based on frequency domain analysis

Abstract

A kind of X-ray telescope support truss hierarchical thermal control method and system based on frequency domain analysis, the method includes establishing physical domain heat transfer model and carrying out model reduction, extracting first-order linear characteristic equation;Through the frequency domain analysis of characteristic equation, the transfer law of equivalent heat transfer coefficient G and equivalent absorption coefficient λ to different frequency band thermal disturbance is quantitatively revealed, and the design target of passive insulation and active control is determined accordingly;Based on the conclusion of frequency domain analysis, a two-stage passive suppression system composed of individual isolation and system isolation is constructed to attenuate low-frequency platform disturbance, while the upper and lower datum plates are optimized for differential passive thermal characteristics, and an active control loop operating at a specific high frequency band is configured, ultimately forming a frequency domain collaborative temperature control mechanism of passive low-frequency suppression and active high-frequency control.The present application realizes ultra-high temperature stability at low energy consumption cost in extremely complex thermal environment, effectively solving the problem that the precision and energy consumption of traditional thermal control method are difficult to be considered in through structure.

Description

Technical Field

[0001] This invention belongs to the field of spacecraft thermal control technology, specifically relating to a hierarchical thermal control method and system for the support truss of a through-type X-ray space telescope based on frequency domain analysis. It is applicable to solving the problem of high-stability temperature control of precision instruments with integrated configurations such as "full-cabin through-type" in orbit. Background Technology

[0002] Space X-ray astronomy observations are a crucial means of exploring extreme cosmological processes, and these observations must be carried out using space telescopes. The core of such telescopes—the X-ray focusing optics and its detectors—has extremely stringent requirements for on-orbit temperature stability. Even minute temperature fluctuations can cause the optics to defocus and the optical axis to shift, directly affecting image quality and scientific output.

[0003] To ensure thermal stability, most current high-precision optical satellites adopt a "compartmental design" as the cornerstone of their thermal control architecture. This approach separates the payload compartment from the satellite platform compartment through physical isolation, supplemented by highly efficient multi-layered thermal insulation materials, aiming to create a quasi-static thermal environment for the payload with minimal interference from the platform's internal components. Missions such as China's Insight-HXMT (Hard X-ray Modulation Telescope) and international missions like Astro-E have successfully utilized this strategy, primarily relying on passive thermal control methods to achieve a stable temperature field for the payload.

[0004] However, in pursuit of ultimate structural rigidity and imaging accuracy, the design of next-generation space telescopes is showing a new trend, with the emergence of a "through-module" support truss configuration, such as that used by the X-ray telescope (FXT) accompanying the Einstein Probe (EP) satellite. In this configuration, the support structure connecting the optical reference plate and the detector reference plate runs directly through the platform module and the payload module, forming an integrated layout with deep coupling between the payload and the platform. This change poses a fundamental challenge to the traditional "module isolation" thermal control paradigm, specifically manifested in the following ways:

[0005] 1. Traditional methods fail: The premise of physical isolation no longer exists. Low-frequency temperature fluctuations inside the platform cabin can be directly and efficiently transferred to the temperature-sensitive optical reference surface through solid heat conduction that penetrates the structure. Traditional heat insulation panels are rendered ineffective in this case.

[0006] 2. Insufficient understanding of disturbances: Existing thermal control designs rely heavily on time-domain analysis and engineering experience, lacking a deep understanding of the transmission patterns of complex thermal disturbances (such as internal equipment power consumption and external heat flow through the track) in the through-structure. Because the transmission characteristics of disturbances from different sources and at different frequency bands cannot be distinguished in the frequency domain, control strategy design lacks precise theoretical guidance, making it difficult to effectively intervene in the most critical frequency bands.

[0007] Lack of control coordination: In existing technologies, passive insulation and active temperature control are often relatively independent design components, lacking deep coordination. This may lead to either excessive thermal inertia and slow response of the system, or the active control having to bear a large basic thermal load, resulting in huge energy consumption, controller saturation, or even the introduction of new temperature fluctuations, thus falling into the dilemma of being unable to achieve both "control accuracy" and "system energy consumption".

[0008] In summary, existing thermal control technologies based on "compartmental isolation" and "passive" approaches have shown systemic limitations in the face of the deeply coupled and dynamically random thermal environment of a "through-cabin" precision structure. Therefore, there is an urgent need in this field for a novel precision thermal control theory and method that can fundamentally analyze the disturbance transmission mechanism and thereby achieve collaborative, efficient, and precise thermal control design to ensure the detection capabilities of the next generation of high-performance space telescopes. Summary of the Invention

[0009] The purpose of this invention is to overcome the shortcomings of existing thermal control technologies and provide a graded thermal control method and system for the support truss of a through-hole X-ray space telescope based on frequency domain analysis. By establishing a complete technical chain from "model order reduction - frequency domain analysis - graded design - experimental verification", the frequency domain transmission law of thermal disturbances is first theoretically revealed, and then a composite thermal control system of "graded suppression - zoned control" is constructed accordingly. This system achieves precise compensation for mid-to-high frequency residual disturbances and setpoints through a two-stage passive thermal insulation targeted attenuation platform for low-frequency thermal disturbances, and through the optimization of passive thermal characteristics of upper and lower reference plates and the coordinated design of active control loops. Ultimately, under extremely complex thermal environments, it achieves global thermal stability of the support truss and ultra-high temperature uniformity and stability of key parts with low energy consumption, fundamentally solving the problems of control blind spots, accuracy and energy consumption contradictions that exist in traditional methods when dealing with "through-hole" structures.

[0010] To achieve the above-mentioned objectives, the technical solution of the present invention includes the following:

[0011] A graded thermal control method for the support truss of a through-hole X-ray space telescope based on frequency domain analysis, characterized by including:

[0012] Step 1. Quantifying the Characteristics of Thermal Disturbance Transfer Based on Frequency Domain Analysis. First, a physical domain heat transfer model of the supporting truss is established and spatially discretized. Then, through a model reduction process, the high-order nonlinear discretized model is simplified into a first-order linear characteristic equation, the general form of which is:

[0013]

[0014] In the formula, C is the heat capacity of the characteristic model, J / K; T0 is the characteristic model temperature (K); T0 is the characteristic model thermal environment temperature (including radiative and conductive environments) (K); G is the heat transfer coefficient between the characteristic model and the thermal environment (W / K); λ is the equivalent absorption coefficient, ranging from 0 to 1.

[0015] The core feature lies in: performing a Laplace transform on the characteristic equation to derive the system's response to environmental temperature disturbances and external heat flow disturbances. transfer function and And through its amplitude-frequency characteristics and This study quantitatively analyzes the transmission and attenuation patterns of thermal disturbances in different frequency bands, providing a precise frequency domain theoretical basis for all subsequent thermal control designs.

[0016] Step 2. Hierarchical passive suppression characteristics for low-frequency disturbances on the platform

[0017] Based on the above frequency domain analysis, "reducing the equivalent heat transfer coefficient" Based on the conclusion that it can effectively suppress low-frequency ambient temperature disturbances, a two-stage passive insulation system was designed: .

[0018] Individual isolation: Each support rod is independently covered with a high-performance multi-layer thermal insulation component, which directly reduces its radiative heat transfer coefficient with the platform cabin environment, and achieves first-order attenuation of low-frequency disturbances on the platform.

[0019] System isolation: In addition to the individual isolation, the entire supporting truss is wrapped with a complete system-level multi-layer thermal insulation component, forming a global thermal protection boundary. This double-shields the radiative temperature fluctuations of the platform cabin, further reducing the overall equivalent heat transfer coefficient between the truss and the external environment at the system level. .

[0020] The system-level multi-layer thermal insulation component is constructed as a dome structure, the edges of which are thermally connected to the outer edges of the upper and lower reference plates by pressing or sewing, thereby enclosing the entire truss in a relatively closed, highly thermally insulated cavity, leaving only the necessary optical path.

[0021] Step 3. Precisely adjust the partitioning features of the upper and lower reference plates.

[0022] Differentiated thermal control designs are implemented based on the different thermal environments and performance indicators of the optical reference plate and the detector reference plate:

[0023] Passive thermal property optimization: For the upper optical reference plate, its surface optical properties are optimized by covering it with a thermal insulation layer to significantly reduce its equivalent absorption coefficient of external heat flow. For the lower detector reference plate, its thermal insulation performance with the platform cabin environment is optimized through the thermal insulation layer covering its surface, thereby significantly reducing its equivalent heat transfer coefficient. .

[0024] Active control system: Multiple electric heaters and high-precision temperature sensors are arranged on the inner side of the upper and lower reference plates to form an independent closed-loop control loop; the active control system is configured to focus on compensating for mid-to-high frequency residual disturbances that have not been completely filtered out by passive measures based on the frequency domain analysis conclusions, and to perform precise setpoint tracking, while avoiding counteracting low-frequency large-amplitude disturbances that have been suppressed by passive measures.

[0025] Step 4. Passive and Active Frequency Domain Co-design Features

[0026] The core feature lies in the fact that the passive suppression and active control are designed collaboratively based on frequency domain characteristics:

[0027] The two-stage passive insulation system reduces the equivalent heat transfer coefficient. It is mainly responsible for suppressing low-frequency bands (e.g. to The platform temperature fluctuates.

[0028] The passive thermal characteristic optimization is achieved by reducing the equivalent absorption coefficient. It is mainly responsible for suppressing low-frequency bands such as orbital period (e.g. to External heat flow disturbance.

[0029] The active control system, by virtue of its Its efficient heat injection capability and high bandwidth are limited to effective frequency bands (e.g., to It operates within the range to compensate for residual mid-to-high frequency disturbances.

[0030] This division of labor based on frequency response characteristics forms a collaborative mechanism of "passive suppression and active fine-tuning," achieving a balance between high control precision and low operating energy consumption.

[0031] Furthermore, the frequency domain analysis in step 2 specifically includes:

[0032] Plotting different equivalent heat transfer coefficients G i The environmental temperature disturbance transmission characteristic curves and the equivalent absorption coefficients λ are shown. i External heat flow disturbance transfer characteristic curve;

[0033] Based on the temperature control requirements of the supporting truss, the equivalent absorption coefficient λ required to achieve the target is read from the curve and determined. i and equivalent absorption coefficient λ iThe specific target value to be attenuated, and the frequency band range that the active control system should switch into.

[0034] Furthermore, the multi-layer thermal insulation components used in the individual isolation system in step 3 have an equivalent emissivity controlled below 0.03.

[0035] Furthermore, the passive thermal characteristic optimization in step 4 is achieved by covering the surface of the upper optical reference plate or the lower detector reference plate with a heat insulation layer having a specific number of layers and material. The heat insulation layer can change the solar absorptivity or infrared emissivity of the surface of the upper optical reference plate and the lower detector reference plate, thereby independently optimizing their equivalent absorption coefficient λ or equivalent absorption coefficient λ to the target value determined in step 2.

[0036] Second, the present invention also provides a graded thermal control system for the support truss of a through-type X-ray space telescope based on frequency domain analysis, for implementing the above method, characterized in that it includes:

[0037] The theoretical analysis module is used to generate frequency domain design parameters, including the target value of the equivalent heat transfer coefficient G, the target value of the equivalent absorption coefficient λ, and the active control operating frequency band.

[0038] A graded passive suppression module, along with the theoretical analysis module, is used to receive the target value of the equivalent heat transfer coefficient G; the graded passive suppression module includes:

[0039] Multiple individual multilayer thermal insulation components, each of which independently covers the outer surface of one of the support rods, are used to reduce local radiative heat transfer between a single support rod and the surrounding environment;

[0040] A system multi-layer thermal insulation assembly covers the exterior of the entire support truss, which consists of the upper optical reference plate, the lower detector reference plate, and multiple support rods, forming a global thermal protection boundary. The individual multi-layer thermal insulation assemblies and the system multi-layer thermal insulation assembly structurally overlap and functionally cooperate to increase the overall equivalent heat transfer coefficient G of the support truss. N Reduced to the target value of the equivalent heat transfer coefficient G;

[0041] A zone-based precise control module, connected to the theoretical analysis module, is used to receive the target value of the equivalent absorption coefficient λ and the active control operating frequency band; the zone-based precise control module includes:

[0042] An upper passive heat insulation layer is set on the upper optical reference plate and its equivalent absorption coefficient λ reaches the target value of the equivalent absorption coefficient λ.

[0043] The lower passive insulation layer is set on the lower detector reference plate and its equivalent heat transfer coefficient G reaches the target value of the equivalent heat transfer coefficient G.

[0044] A multi-channel electric heater and a corresponding temperature sensor are respectively installed on the inner side of the upper and lower reference plates, and an independent closed-loop control loop connects the temperature sensor and the heater; the bandwidth of the closed-loop control loop is configured to be within the active control operating frequency band.

[0045] The collaborative control module, connected to both the hierarchical passive suppression module and the zoned precise control module, is configured as follows:

[0046] Based on the frequency domain design specifications, monitor whether the actual equivalent heat transfer coefficient G of the graded passive suppression module reaches the target value of the equivalent heat transfer coefficient G;

[0047] Based on the frequency domain design specifications, monitor whether the actual equivalent absorption coefficient λ of the upper passive insulation layer and the actual equivalent heat transfer coefficient G of the lower passive insulation layer in the partitioned precise control module have reached their respective target values.

[0048] According to the frequency domain design specifications, a bandwidth configuration command is sent to the closed-loop control loop in the partitioned precision control module to ensure that it operates strictly within the active control operating frequency band. Those skilled in the art will design the crossover frequency (0dB point) of the PID controller near the center frequency (e.g., 0.1Hz) of the active control operating frequency band and ensure that its phase margin is greater than 60° to ensure that the loop has stable gain and good dynamic response within the frequency band, while avoiding unnecessary response to low-frequency disturbances (<10^-2 Hz) that have been effectively suppressed by passive heat insulation.

[0049] The working states of the hierarchical passive suppression module and the zoned precise control module are coordinated to form a collaborative working mode of passively suppressing low frequencies and actively controlling high frequencies, thereby achieving complete suppression of thermal disturbances across the entire frequency band of the support truss.

[0050] Furthermore, the individual multilayer thermal insulation component consists of 15 alternating layers of low-emissivity polyimide film and nylon mesh spacer layers.

[0051] Furthermore, the system's multi-layer thermal insulation component is an integrated cover-like structure that covers the entire outer contour of the supporting truss, and its number of layers and materials may be the same as or different from those of the individual multi-layer thermal insulation component.

[0052] Furthermore, the upper passive heat insulation layer is a multi-layer heat insulation component with low solar absorptivity, used to reduce the equivalent absorption coefficient λ of the upper optical reference plate to external space heat flow; the lower passive heat insulation layer is a multi-layer heat insulation component with low infrared emissivity, used to reduce the equivalent heat transfer coefficient G between the lower detector reference plate and the platform cabin environment.

[0053] Furthermore, the independent closed-loop control loop is a high-precision digital PID control loop, whose proportional, integral, and derivative parameters are tuned according to the active control operating frequency band.

[0054] Furthermore, the collaborative control module includes:

[0055] The first monitoring unit has its input end connected to the status output end of the graded passive suppression module, and is used to obtain the measured value of the total equivalent heat transfer coefficient G of the support truss in real time.

[0056] The second monitoring unit has its input end connected to the status output end of the partition precision control module, and is used to obtain the measured value of the equivalent absorption coefficient λ of the upper optical reference plate and the measured value of the equivalent heat transfer coefficient G of the lower detector reference plate in real time.

[0057] The comparison unit has a first input terminal connected to the output terminal of the first monitoring unit, a second input terminal connected to the output terminal of the second monitoring unit, and a third input terminal connected to the output terminal of the theoretical analysis module, and is used to compare each measured value with the corresponding frequency domain design index.

[0058] The instruction generation unit has its input terminal connected to the output terminal of the comparison unit, and its output terminal connected to the control terminal of the hierarchical passive suppression module and the control terminal of the partitioned precise control module, respectively. It is used to generate and send adjustment instructions based on the comparison results to ensure that the system always operates in the cooperative state specified by the frequency domain design specifications.

[0059] Compared with the prior art, the present invention has the following beneficial effects:

[0060] 1) The frequency domain analysis system is systematically introduced into the thermal control design of complex spatial structures. Through model order reduction and transfer function analysis, the originally ambiguous thermal disturbance transmission process is transformed into a clear and quantifiable frequency domain spectrum. This allows designers to "see" in which frequency band the disturbance is at work, and which measures are most effective in which frequency band. This provides a precise and quantitative theoretical basis for thermal insulation design, surface optimization, and controller parameter tuning, completely eliminating the blind spots and over-reliance on experience in traditional design.

[0061] 2) Through a collaborative mechanism of "passively suppressing low frequencies and actively controlling high frequencies," optimal division of labor in thermal control tasks is achieved. Passive measures handle the most energy-intensive low-frequency, high-amplitude basic thermal load in a zero-energy-consumption manner, while the active system is able to operate with a "light load," requiring only a small amount of energy for fine compensation in the mid-to-high frequency range. This design enables the system to achieve ultra-high temperature stability while maintaining a stable and low level of active heating power, fundamentally breaking through the bottleneck of "high precision inevitably means high energy consumption" in traditional solutions. It achieves a balance between control precision and system energy consumption, which is of great significance for energy-intensive aerospace missions.

[0062] 3) Because the passive insulation system forms a robust basic thermal protection layer, it greatly smooths out the impact of drastic fluctuations in the external thermal environment on core components, significantly reducing the sensitivity of the entire thermal control system to external disturbances (such as attitude maneuvers) and internal disturbances (such as sudden changes in equipment power consumption). The active control system does not need to frequently and significantly adjust its output to cope with these changes, thereby greatly enhancing the system's stability and robustness, avoiding the risks of controller saturation and system oscillation, and ensuring the reliability of long-term on-orbit operation.

[0063] 4) It solves the problem of the specific configuration of "full-module penetration," but the resulting technical route of "model reduction-frequency domain analysis-hierarchical design-experimental verification" has high universality. This methodology can be extended to the thermal control design of other new space science payloads (such as large X-ray observatories and space interferometers) that face deep-coupled thermal disturbances and have high stability requirements, providing a reliable technical path and engineering example that has been tested in practice for the thermal control of future high-performance space exploration missions in my country and even internationally. Attached Figure Description

[0064] Figure 1 This is a schematic diagram of the EP satellite structure according to an embodiment of the present invention;

[0065] In the diagram, 100 represents the EP satellite body, 101 represents the support rod, 102 represents the optical reference plate, 103 represents the detector reference plate, 200 represents the payload carried by the satellite, 201 represents the satellite platform, 303 represents the external radiative heat flow, and 304, 305, and 306 represent the radiative heat flow from the satellite platform (in different directions).

[0066] Figure 2 This is a graph showing the spatial heat flux density absorbed by the satellite in the +X, -X, +Y, -Y, +Z, and -Z directions under the conventional measurement mode in this embodiment of the invention.

[0067] Figure 3In the frequency domain analysis section of this invention, (a) is an analysis curve of the environmental temperature disturbance transmission characteristics under different equivalent heat transfer coefficients G, and (b) is an analysis curve of the external heat flow disturbance transmission characteristics under different equivalent absorption coefficients λ.

[0068] Figure 4 This is a schematic diagram of layered thermal control according to an embodiment of this application.

[0069] In the diagram, 400 represents the system thermal protection layer, 401 represents the individual thermal protection layer, 201 represents the satellite platform, 501 represents the multi-layer thermal insulation component, 101 represents the support rod, and 2 represents thermal disturbance.

[0070] Figure 5 This is a schematic diagram of the graded thermal control according to an embodiment of this application.

[0071] In the diagram, 700 represents the reference plate, 501 represents the multi-layer thermal insulation component, 601 represents the heating circuit, 602 represents the temperature sensor, 1 represents heat injection, and 2 represents thermal disturbance.

[0072] Figure 6 This is a temperature stability curve of each measuring point on the support rod obtained by vacuum thermal testing in an embodiment of the present invention.

[0073] Figure 7 This is a temperature stability curve of each measuring point on the optical reference plate obtained by vacuum thermal testing in an embodiment of the present invention.

[0074] Figure 8 This is a temperature stability curve of each measuring point on the detector reference plate obtained by vacuum thermal testing in an embodiment of the present invention.

[0075] Figure 9 This is a temperature gradient distribution diagram of the entire supporting truss obtained by vacuum thermal testing in an embodiment of the present invention.

[0076] Figure 10 This is a temperature gradient stability curve of the support truss obtained by vacuum thermal testing in an embodiment of the present invention.

[0077] Figure 11 This is a flowchart illustrating the overall steps of the hierarchical thermal control method for the support truss of a through-type X-ray space telescope based on frequency domain analysis, as described in this invention. Detailed Implementation

[0078] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It is to be understood that the specific embodiments described herein are merely illustrative of the invention and not intended to limit it. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without inventive effort are within the scope of protection of this invention.

[0079] Example 1

[0080] This embodiment takes the support truss of the EP satellite's follow-up X-ray telescope (FXT) as the application object, and elaborates in detail the specific implementation process of the hierarchical thermal control method and system for the support truss of a through-type X-ray space telescope based on frequency domain analysis provided by the present invention.

[0081] 1. Temperature control requirements and thermal disturbance analysis

[0082] The FXT support truss is the core load-bearing structure of the follow-up X-ray telescope. Its main function is to provide high-precision and high-stability installation references and structural support for the FXT focusing lens assembly and detector assembly. Its thermal-structural stability directly determines the telescope's imaging quality and pointing accuracy in orbit.

[0083] The truss is located at the very center of the satellite and employs a unique full-module through-type configuration. Its upper optical reference plate is thermally insulated and mounted to the overall payload support structure outside the satellite platform using 10mm thick fiberglass thermal pads and low thermal conductivity titanium alloy screws. The lower detector reference plate and the intermediate support rods are based inside the satellite platform module and do not contact the module itself. This special layout allows its thermal environment to span between the payload module and the platform module, such as… Figure 1 As shown.

[0084] To ensure the superior performance of the EP satellite payload FXT, extremely stringent and precise temperature control parameters were imposed on its support structure. These parameters directly contribute to ensuring optical performance.

[0085]

[0086] The thermal environment faced by the FXT support truss is a highly dynamic and non-uniform distributed disturbance field that couples external heat flow with the power consumption of equipment inside the cabin. Its complexity far exceeds the load of traditional compartment design.

[0087] 1) Internal Disturbances: Non-uniform time-varying thermal field within the platform module. Based on the lower detector reference plate and support rods within the platform module, the system is primarily affected by the direct thermal environment inside the module. The module is filled with various electronic components (such as attitude and orbit control instruments, spacecraft computers, power controllers, etc.), whose spatial arrangement is disordered, and whose power consumption exhibits significant intermittent fluctuations. This results in a complex radiative-conductive mixed thermal boundary within the platform module, with uneven temperature distribution that varies over time, becoming a continuous and unpredictable source of internal disturbances acting on the lower part of the truss.

[0088] 2) External Disturbances: The highly dynamic space thermal environment. The thermally insulated optical reference plate mounted on the upper part of the payload bay is directly exposed to the external space heat flux. The absorbed direct solar radiation heat flux q... s Earth's albedo radiation heat flow q a and Earth's infrared radiation heat flow q e .

[0089] The scientific mission of the Einstein Probe satellite required it to perform frequent attitude maneuvers. For example... Figure 2 As shown, in conventional sky survey mode, satellites need to continuously change attitude at fixed points in multiple orbits; in follow-up observation mode, even more random and rapid maneuvers occur. This causes the external heat flow it faces to no longer change in a periodic and regular manner around a single orbit, but rather exhibits strong randomness and unpredictability.

[0090] 3) Disturbance Coupling and Extreme Operating Conditions. More complexly, internal and external disturbances are deeply coupled. The satellite's attitude maneuvers (external factors) directly trigger synchronous changes in the operating states of multiple subsystems within the platform cabin, such as momentum wheel speed adjustments, gyroscope activation, solar drive mechanism (SADA) orientation to the sun, and power controller load changes. This means that a single change in external orientation will simultaneously disturb both the external heat flow boundary and the internal heat source distribution, creating an extreme thermal condition characterized by "internal and external constraints and dynamic linkage."

[0091] In summary, the FXT support truss faces an extreme thermal environment that combines the randomness and complexity of external heat flow with the non-uniformity and time-varying nature of power consumption of in-cabin equipment, and these two aspects are deeply coupled. This presents unprecedented challenges to its precision thermal control and highlights the urgency and necessity of developing a new approach that transcends traditional paradigms.

[0092] 2. Physical Domain Modeling

[0093] To achieve an accurate description of the truss temperature field, a physical domain heat transfer model is first established based on heat transfer theory. This model consists of internal heat conduction control equations and boundary conditions (contact thermal boundary and mixed radiation boundary), and is a nonlinear, coupled continuous system.

[0094] To facilitate numerical simulation and frequency domain analysis, the continuous model is spatially discretized using the thermal network method. The upper optical reference plate, the middle support rod, and the lower detector reference plate are discretized into multiple nodes, and the discrete heat transfer equations are established as shown below.

[0095] (1)

[0096] Where T(r,t) represents the temperature field at spatial location r and time t, in K; ρ(r), c(r), and k(r) are the location-dependent densities (unit: kg / m³). 3 The specific heat capacity (J / kg / K) and thermal conductivity (W / K / m) reflect the differences in material properties between different domains (reference plate, strut); q(r, t) is the internal heat source, and in this study the gantry is a passive component, W; This represents the 3D gradient differential operator.

[0097] Equation (1) describes the evolution of the internal temperature of the structure with space and time under the combined effects of material density, specific heat capacity, and thermal conductivity. The truss itself is a passive component, therefore the governing equations do not include internal heat source terms. The system undergoes complex heat exchange with the external environment through its boundaries. Its outer surface mainly faces two types of boundary conditions:

[0098] 1) Contact thermal boundary: At the mechanical mounting interface between the truss and the satellite platform, heat is exchanged through solid contact conduction, the intensity of which is determined by the contact heat transfer coefficient.

[0099] (2)

[0100] In the formula, h c The thermal conductivity and heat transfer coefficient are related to the specific installation method of the rack, expressed in W / (m·K); T c Let K be the temperature at the contact boundary.

[0101] 2) Hybrid Radiation Boundary: Energy is exchanged between the truss surface and the space environment through thermal radiation; this term is highly nonlinear. Furthermore, this boundary also incorporates external heat flows such as direct solar radiation, Earth's albedo radiation, and Earth's infrared radiation, as well as the input power of the active thermally controlled electric heater, resulting in:

[0102] (6)

[0103] In the formula, For the surface normal of the object; T e σ is the ambient temperature, K; σ is the Stefan-Boltzmann constant, W / (m²). 2 ·K 4 ); ε is the emissivity of the truss surface; β is the radiation angle coefficient between the truss surface and the radiative thermal environment; qh W represents the heat flux generated by the electric heater on the surface of the reference plate.

[0104] The aforementioned governing equations and boundary conditions together constitute a nonlinear, coupled continuous system that accurately describes the heat transfer process of the truss in a real environment.

[0105] To facilitate numerical simulation and thermal control design, the aforementioned continuous model (the internal heat conduction equation described by equation (1) and the boundary conditions described by equations (2) and (3)) needs to be spatially discretized. Specifically, the upper optical reference plate, the middle support rod, and the lower detector reference plate are discretized into N1, N2, and N3 nodes respectively using the thermal network method. The calculation formula for the upper optical reference plate is as follows:

[0106] (4)

[0107] In the formula, The heat capacity of the i-th node of the optical reference plate is given in J / K. , Let be the temperatures of the i-th and j-th nodes of the optical reference plate, respectively, in K; Let be the emissivity between the i-th node on the optical reference plate and the j-th node in the radiative thermal environment, in W / K. 4 ; Let be the thermal conductivity between the i-th node and the j-th node of the optical reference plate, in W / K; The thermal conductivity (W / K) is the thermal transfer coefficient between the i-th node of the optical reference plate and the j-th node of the contact boundary; Q is the sum of external heat flows acting on the optical reference plate (direct solar radiation heat flow q). s Earth's albedo radiation heat flow q a and Earth's infrared radiation heat flow q e W; u is the heating power of the electric heater mounted on the optical reference plate; Nr1 and Nc1 are the discrete number of nodes in the radiant heat environment and the contact boundary, respectively.

[0108] The discrete heat transfer equation for the intermediate strut is as follows:

[0109] (5)

[0110] In the formula, Let J / K be the heat capacity of the i-th node of the strut. , Let K be the temperatures of the i-th and j-th nodes of the strut, respectively. Let W / K be the radiation coefficient between the i-th node on the strut and the j-th node of the radiative thermal environment. 4 ; Let be the thermal conductivity and heat transfer coefficient between the i-th node and the j-th node of the strut body, in W / K; Let be the thermal conductivity (W / K) between the i-th node of the strut and the j-th node of the contact boundary; Nr2 and Nc2 are the discrete number of nodes in the radiative thermal environment and the contact boundary, respectively.

[0111] The discrete heat transfer equations for the lower detector reference plate are as follows:

[0112] (6)

[0113] In the formula, Let be the heat capacity of the i-th node of the detector reference plate, in J / K; , Let be the temperatures of the i-th and j-th nodes of the detector reference plate, respectively, in K; Let be the emissivity between the i-th node on the detector reference plate and the j-th node in the radiative thermal environment, in W / K. 4 ; Let be the thermal conductivity between the i-th node and the j-th node of the detector reference plate, in W / K; denoted as , where is the thermal conductivity / heat transfer coefficient between the i-th node of the detector reference plate and the j-th node of the contact boundary, in W / K; u is the heating power of the electric heater mounted on the detector reference plate, in W; Nr3 and Nc3 are the discrete number of nodes in the radiative thermal environment and the contact boundary, respectively.

[0114] 3. Feature Model Extraction

[0115] The high-order discrete model described above is reduced in order to extract the core dynamic features governing the thermal behavior of the truss. The specific process is as follows:

[0116] 1) Equivalent aggregation of key components: Based on the structural symmetry and thermal characteristics of each component of the truss, equivalent aggregation is performed. The upper optical reference plate, the middle support rod assembly, and the lower detector reference plate, which have similar thermal characteristics, are each equivalent to a single node, and their heat capacity is taken as the sum of the corresponding components.

[0117] 2) Radiation and conduction normalization: To achieve frequency domain analysis, the two heat transfer methods of heat conduction and heat radiation are integrated, and the radiation heat transfer terms in equations (4), (5), and (6) are mathematically transformed as follows:

[0118] (7)

[0119] 3) Combining and Equivalent Heat Sources: Multiple external heat flows (external space heat flow and electric heater power) acting on the same component are combined into an equivalent heat source, and an equivalent heat flow absorption coefficient λ (ranging from 0 to 1) is introduced to characterize the final absorption efficiency of the component for the equivalent heat source.

[0120] (8)

[0121] Based on the above three steps, and combining equations (4), (5), (6), (7), and (8), the complex high-order nonlinear model can be successfully reduced to a simple first-order characteristic equation, the general form of which is:

[0122] (9)

[0123] In the formula, C is the heat capacity of the characteristic model, J / K; T0 is the characteristic model temperature (K); T0 is the characteristic model thermal environment temperature (including radiative and conductive environments) (K); G is the heat transfer coefficient between the characteristic model and the thermal environment (W / K); λ is the equivalent absorption coefficient, ranging from 0 to 1.

[0124] This characteristic equation profoundly reveals that the thermal response of the FXT support truss is essentially the result of a dynamic balance among its effective heat capacity C, its coupling strength with the environment G, and its absorption efficiency of external power λ.

[0125] 4. Frequency Domain Analysis

[0126] By performing a Laplace transform on the characteristic equation (9), it can be transformed from the time domain to the complex frequency domain, and the temperature can be derived from this. With respect to ambient temperature T0 and external heat flow Transfer function between:

[0127] (10)

[0128] Wherein, the transfer function H1 is the thermal ambient temperature T0 and the characteristic model temperature. The transfer relationship between them, with transfer function H2 being an external heat source. With characteristic model temperature The transmission relationship between them.

[0129] make The amplitude-frequency response of the system transfer function can be obtained:

[0130] (11)

[0131] Where ω is the angular frequency.

[0132] To visually demonstrate the frequency domain characteristics of thermal disturbance propagation, Figure 3 The characteristics of ambient temperature disturbance propagation are given. and external heat flow disturbance transfer characteristics The figure shows a double logarithmic coordinate curve, which clearly reveals the propagation law of thermal disturbance in different frequency bands and provides quantitative guidance for thermal control design.

[0133] Based on the above analysis, for a given research object where the heat C is a fixed quantity, the amplitude attenuation ratio of the transfer function H1 is... It depends on the characteristic model's heat transfer coefficient G with the external environment and the angular frequency ω of the thermal disturbance from the environment; the amplitude attenuation ratio of the transfer function H2. The external equivalent absorption coefficient λ and the angular frequency ω from the environmental thermal disturbance. The specific rules are as follows:

[0134] 1) Environmental disturbance attenuation law: |H1| decreases with increasing frequency, indicating that the system has a natural attenuation effect on high-frequency environmental temperature disturbances. However, in the low-frequency range (ω→0), |H1|→1, the system has almost no attenuation effect on environmental temperature disturbances, which means that low-frequency fluctuations in platform compartment temperature will have a decisive impact on truss temperature stability;

[0135] 2) Frequency domain interpretation of thermal insulation design: |H1| is directly related to the equivalent heat transfer coefficient G. Reducing G (i.e., enhancing thermal insulation) can significantly reduce |H1| throughout the entire frequency band, which provides a theoretical basis for suppressing environmental temperature disturbances through thermal insulation design;

[0136] 3) External heat flow disturbance response characteristics: |H2| is inversely proportional to frequency in the low-frequency range, indicating that the system is extremely sensitive to low-frequency external heat flow disturbances (such as orbital period changes, on the order of 0.1 mHz). However, |H1| can be directly reduced by decreasing the equivalent absorption coefficient λ, which guides us to weaken the influence of external heat flow through surface optimization design;

[0137] 4) Frequency domain advantages of active control: |H2| decays rapidly in the high-frequency band, indicating that the high-frequency heat source (active heater, on the order of 1Hz) has a limited impact on the system temperature. This characteristic ensures that active heating control will not cause system oscillations, making it very suitable for precise temperature fine-tuning.

[0138] 5. Hierarchical thermal disturbance suppression design

[0139] To fundamentally attenuate internal thermal disturbances from the platform compartment, based on the key conclusion of frequency domain analysis—reducing the system's equivalent heat transfer coefficient G—is the most effective way to suppress low-frequency ambient temperature disturbances. Figure 4 As shown, a two-stage passive insulation system consisting of "individual isolation" and "system isolation" was designed.

[0140] 1) Individual Isolation: This stage targets the 12 carbon fiber support rods that constitute a significant thermal coupling path. Each rod is independently encased in a high-performance thermal insulation component consisting of 15 layers of low-emissivity polyimide film and nylon mesh spacers. The equivalent emissivity of this component is strictly controlled below 0.03. By introducing high radiative thermal resistance into each support rod, the radiative heat transfer coefficient between the support rod nodes and the platform cabin environment nodes is significantly reduced directly in the thermal network model, achieving component-level first-order attenuation of low-frequency temperature disturbances in the platform cabin.

[0141] 2) System Isolation: Building upon individual isolation, a global static thermal protection boundary is established by encasing the entire FXT truss in a complete 15-layer thermal insulation "heat shield." Its core mechanism lies in dual shielding: significantly reducing direct radiative heat transfer between the platform cabin's inner walls and key truss components, while simultaneously creating a quasi-static local microenvironment around the truss with significantly smoothed temperature fluctuations. This transforms the thermal boundary conditions acting on the truss from drastically fluctuating platform cabin temperatures to a more stable equivalent temperature, reducing the overall equivalent heat transfer coefficient G between the truss and the external environment at the system level, thereby achieving effective system-level attenuation of low-frequency thermal disturbances in the platform cabin.

[0142] The two-level isolation constitutes a deep thermal protection system, which theoretically ensures that internal thermal disturbances are attenuated in multiple layers when they are transmitted to key parts of the truss, laying a stable thermal environment foundation for subsequent active control.

[0143] 6. Precise temperature control design for different zones

[0144] To address the extremely high temperature gradient and stability requirements of the upper and lower reference plates, a "zoned precise control" scheme was designed. This involves passively optimizing the system's inherent frequency domain characteristics, followed by active control for final correction. Figure 5 As shown, a collaborative mechanism of "passively suppressing low frequencies and actively controlling high frequencies" is formed.

[0145] 1) Passive thermal characteristic optimization: The frequency domain response characteristics of the upper and lower reference plates are specifically improved through differentiated insulation layer design. For the upper optical reference plate, the multi-layered insulation coating significantly reduces the equivalent absorption coefficient λ of external heat flow. Based on the transfer function relationship... This directly reduces the impact of low-frequency external heat flow disturbances, such as orbital period changes, on the plate temperature. For the lower detector reference plate, the multi-layered outer coating effectively reduces the equivalent heat transfer coefficient G between it and the platform cabin environment. Based on the transfer function relationship... This significantly reduced low-frequency temperature fluctuations from the platform compartment.

[0146] 2) Active Control System Design: Precise control is implemented based on optimized passive thermal characteristics. Five electric heater actuators are arranged on the inner sides of the upper and lower reference plates, with a corresponding λ ≈ 1, ensuring efficient heat injection and providing an ideal execution means for precise control in the high-frequency range. At the same time, correspondingly arranged high-precision thermistors form a complete temperature measurement network, which, combined with an independent high-precision digital PID control loop, achieves precise compensation for residual fluctuations, especially mid-to-high frequency disturbances.

[0147] 3) A passive and active frequency domain synergy mechanism is thus established: the passive insulation layer is responsible for suppressing low-frequency, large-amplitude disturbances, fundamentally improving the inherent characteristics of the system by optimizing λ and G parameters; the active electric heating circuit, with its highly efficient heat injection characteristics of λ ≈ 1, focuses on suppressing mid-to-high frequency residual disturbances. This synergistic design of "passively optimizing inherent characteristics and actively compensating for residual fluctuations" achieves the goal of ensuring the extreme temperature control index of the reference plate with minimal control energy consumption.

[0148] Based on a frequency domain analysis-guided hierarchical suppression and zoned control strategy, the aforementioned thermal control design scheme was ultimately formed. This scheme constructs a complete passive thermal protection system through two-stage thermal insulation, and at the same time designs a collaborative control loop of "passive optimization + active compensation" for the upper and lower reference plates, forming a complete thermal control chain from global stability to local precision.

[0149] 7. Satellite vacuum thermal test results

[0150] Under all four extreme operating conditions, the temperature at all measuring points on the 12 support members showed a high degree of consistency. The maximum temperature difference across the entire support member was 1.9 ℃ under low-temperature platform conditions and 2.1 ℃ under high-temperature load conditions, significantly better than the requirement of ≤10 ℃. Meanwhile, the maximum temperature change at any single measuring point under all operating conditions was 3.1 ℃, meeting the temperature stability requirement of ≤±2 ℃.

[0151] The upper optical reference plate performed particularly well, with a maximum temperature gradient of only 0.95 ℃ across all measuring points under different operating conditions, and a maximum temperature change of no more than 1.2 ℃ at a single measuring point. The lower detector reference plate, operating in a more complex thermal environment, exhibited a maximum temperature gradient of 2.3 ℃ and a maximum temperature change of 1.6 ℃ at a single measuring point. Both reference plates met the requirement of ≤4 ℃ for temperature gradient, and the temperature stability of their individual measuring points met the requirement of ≤±2 °C.

[0152] Regarding the overall structural thermal stability, the maximum temperature gradient fluctuation of the entire FXT support truss structure under four operating conditions was 1.4 ℃, meeting the requirement of ≤4 ℃. This indicates that, under complex and deeply coupled internal and external thermal disturbances, the thermal deformation of the entire support structure was effectively controlled through the precision thermal control method proposed in this paper, providing a fundamental guarantee for maintaining the optical axis pointing accuracy and focusing performance of the Wolter-I type focusing optical system.

[0153] The experimental results show that the hierarchical thermal control method and system based on frequency domain analysis proposed in this invention successfully solves the thermal control problem of the "full-cabin through" structure in a complex thermal environment, and achieves ultra-high temperature uniformity and stability far exceeding traditional indicators at the cost of low energy consumption.

[0154] This invention's high-precision active thermal control technology fundamentally overcomes the inherent limitations of passive temperature control strategies, such as uncontrollable temperature, lengthy thermal equilibrium times, and excessive mass costs. Based on the spacecraft's thermal control configuration, a physical model is established to meet the high-precision temperature control requirements, and an innovative "adaptive precision temperature control method with global reduced-order sensing" is proposed. Addressing three core challenges—sparse temperature sensor placement, measurement noise suppression bottlenecks, and the strong nonlinear time-varying characteristics of the thermal system—this method integrates: real-time digital filtering technology (improving the measurement signal-to-noise ratio), a global state reduced-order sensing architecture (overcoming dimensional constraints), and an online key parameter estimator (compensating for nonlinear time-varying characteristics). This constitutes a systematic solution. Simulation verification shows that this method achieves breakthrough improvements in filtering performance, steady-state accuracy, and dynamic response.

[0155] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art can make various improvements and modifications without departing from the spirit and principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A graded thermal control method for the support truss of an X-ray space telescope based on frequency domain analysis, characterized in that, Includes the following steps: Step 1: Establish the characteristic equation describing the thermal dynamic characteristics of the support truss. The characteristic equation includes the equivalent heat transfer coefficient G and the equivalent absorption coefficient λ. Step 2: Perform frequency domain analysis on the characteristic equation and determine the design objectives for passive suppression and active control based on the analysis results; Step 3: Based on the design objectives, construct a passive suppression system to reduce the overall equivalent heat transfer coefficient G of the support truss; Step 4: Based on the design objectives, implement differentiated control for different areas of the support truss. The differentiated control includes passive thermal characteristic optimization and active control loop configuration. Step 5: Through the synergistic operation of the passive suppression system and the differentiated control, the graded suppression of thermal disturbances across the entire frequency band of the support truss is achieved.

2. The graded thermal control method for the support truss of an X-ray space telescope according to claim 1, characterized in that, The characteristic equation in step 1 is obtained by reducing the order of the support truss through physical modeling, and its form is as follows: In the formula, C is the heat capacity of the characteristic model; Temperature is a characteristic model; T0 is the thermal environment temperature of the characteristic model, including the radiative thermal environment temperature and the conductive thermal environment temperature; G is the equivalent heat transfer coefficient; λ is the equivalent absorption coefficient. It is external heat flow.

3. The graded thermal control method for the support truss of an X-ray space telescope according to claim 1, characterized in that, The frequency domain analysis in step 2 specifically includes: Derivation of the characteristic equation for ambient temperature disturbance Amplitude-frequency characteristics and external heat flow disturbance Amplitude-frequency characteristics ; Based on the amplitude-frequency characteristics, the attenuation law of the equivalent heat transfer coefficient G and the equivalent absorption coefficient λ for thermal disturbance transmission in different frequency bands is quantitatively analyzed, and the design target is determined accordingly. The design target includes the target value of the equivalent heat transfer coefficient G and the target value of the equivalent absorption coefficient λ required to suppress low-frequency disturbances, as well as the operating frequency band set for active control.

4. The graded thermal control method for the support truss of an X-ray space telescope according to claim 1, characterized in that, The construction of the passive inhibition system in step 3 specifically includes: Individual isolation, where each support member of the support truss is independently covered with a thermal insulation component; System isolation, with the entire supporting truss encased in system-level thermal insulation components; The individual isolation and the system isolation together constitute a two-level passive inhibition system.

5. The graded thermal control method for the support truss of an X-ray space telescope according to claim 1, characterized in that, The differentiated regulation in step 4 includes: For the upper optical reference plate of the supporting truss, its equivalent absorption coefficient λ is reduced by passive thermal characteristic optimization in order to weaken low-frequency external heat flow disturbance. For the lower detector reference plate of the supporting truss, its equivalent heat transfer coefficient G is reduced by passive thermal characteristic optimization to weaken the temperature disturbance of the low-frequency platform. The active control loop is configured on the upper optical reference plate and the lower detector reference plate respectively to compensate for mid-to-high frequency residual disturbances.

6. The graded thermal control method for the support truss of an X-ray space telescope according to claim 5, characterized in that, The bandwidth of the active control loop is configured to operate within the active control operating frequency band determined in step 2.

7. A graded thermal control system for an X-ray telescope support truss based on frequency domain analysis, characterized in that, include: The theoretical analysis module is used to generate design targets through frequency domain analysis. The design targets include the target value of the equivalent heat transfer coefficient G, the target value of the equivalent absorption coefficient λ, and the active control operating frequency band. A graded passive suppression module, connected to the theoretical analysis module, is used to construct a passive suppression system based on the target value of the equivalent heat transfer coefficient G, so as to reduce the overall equivalent heat transfer coefficient G of the support truss. The zoned precision control module, connected to the theoretical analysis module, is used to implement differentiated control on different regions of the support truss based on the target value of the equivalent absorption coefficient λ and the active control operating frequency band. The differentiated control includes passive thermal characteristic optimization and active control loop configuration. The collaborative control module is connected to the hierarchical passive suppression module and the zoned precise control module respectively, and is used to coordinate the working states of the two to form a collaborative working mode of passively suppressing low frequencies and actively controlling high frequencies.

8. The graded thermal control system for X-ray telescope support truss based on frequency domain analysis according to claim 7, characterized in that, The graded passive suppression module includes: Multiple individual multilayer thermal insulation components, each of which independently covers the outer surface of one support member of the support truss; A multi-layer thermal insulation assembly that covers the entire exterior of the supporting truss; The individual multi-layer thermal insulation components and the system multi-layer thermal insulation components are structurally encased in sequence and functionally synergistic, so that the overall equivalent thermal coefficient of the supporting truss is reduced to the target value of the equivalent heat transfer coefficient G.

9. The graded thermal control system for X-ray telescope support truss based on frequency domain analysis according to claim 7, characterized in that, The precise partition control module includes: The first passive heat insulation layer is set on the upper optical reference plate to make its equivalent absorption coefficient λ reach the target value of the equivalent absorption coefficient λ; The second passive heat insulation layer is set on the lower detector reference plate to make its equivalent heat transfer coefficient G reach the target value of the equivalent heat transfer coefficient G; Multiple electric heaters and corresponding temperature sensors are respectively installed on the inner sides of the upper and lower reference plates, and an independent closed-loop control loop connects the temperature sensors and the heaters; the bandwidth of the closed-loop control loop is configured to operate within the active control operating frequency band.

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